Dynamics of parafermionic states in transport measurements

Abstract

Advances in hybrid fractional quantum Hall (FQH)-superconductor platforms pave the way for realisation of parafermionic modes. We analyse signatures of these non-abelian anyons in transport measurements across devices with ${\mathbb{Z}}_6$ parafermions (PFs) coupled to an external electrode. Simulating the dynamics of these open systems by a stochastic quantum jump method, we show that a current readout over sufficiently long times constitutes a projective measurement of the fractional charge shared by two PFs. Interaction of these topological modes with the FQH environment, however, may cause poisoning events affecting this degree of freedom which we model by jump operators that describe incoherent coupling of PFs with FQH edge modes. We analyse how this gives rise to a characteristic three-level telegraph noise in the current, constituting a very strong signature of PFs. We discuss also other forms of poisoning and noise caused by interaction with fractional quasiparticles in the bulk of the Hall system. We conclude our work with an analysis of four-PF devices, in particular on how the PF fusion algebra can be observed in electrical transport experiments.

References in corpus (13)

• Quantum trajectories and open many-body quantum systems
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Measurement-Only Topological Quantum Computation
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Fractional topological superconductors with fractionalized Majorana fermions
• Luttinger Liquid in Non-equilibrium Steady State
• Commensurate and Incommensurate States of Topological Quantum Matter
• Controlled DC Monitoring of a Superconducting Qubit
• Detecting Majorana modes by readout of poisoning-induced parity flips
• Anyon statistics through conductance measurements of time-domain interferometry
• Topological blockade and measurement of topological charge
• Anomalous periodicity and parafermion hybridization in superconducting qubits

Cited by in corpus (4)

• Engineering a Josephson junction chain for the simulation of the clock model
• Quantum computation with hybrid parafermion-spin qubits
• Signatures of Parafermion Zero Modes in Fractional Quantum Hall-Superconductor Heterostructures
• Can Majorana zero modes in quantum Hall edges survive edge reconstruction?